This theoretical research aims at finding methods of abstract mathematical analysis which can be applied to pharmacokinetics and which may circumvent some of the problems of biological complexity and biological variability and facilitate the use of empirical data to make practical predictions and plan therapeutic regimens. Attention to date has been focused on the principle of superposition for linear pharmacokinetic systems. This has been shown to be usable for predicting patterns of drug accumulation on repetitive dosage, from information on drug levels following a single dose. Mean accumulation levels can also be predicted for certain nonlinear systems, as well as for linear systems. Another area of study has been the transient peak drug levels resulting from rapid intravenous injections; and here it has been shown that, for a given fixed dose, the peak level increases with increasing rate of injection, if "rate of injection" is suitably defined. Further analysis has also been done in an attempt to determine optimal patterns of drug infusions.